Small Sample Null Distribution of Two Nonparametric Tests for Comparing Treatments with a Control in a Two–Way Layout

Abstract

Fligner and Wolfe (1982) and Chakraborti and Desu (1988) propose distribution–free tests for comparing several treatments with a control at b levels of another factor (blocks). Here computer programs written in FORTRAN are developed to calculate the exact null distributions of these test statistics. Tables are generated (available from the authors) for the exact critical values (and probabilities) at a-levels near 0.25, 0.1, 0.05, 0.01 and 0.001 where b(l)5. The tables cover designs where the number of observations in each block, M, ranges from 3 to 10 and the sample sizes for the control group range from 1 to 5 for b1(1)3. For b4 the control sample sizes are all equal and range from 1 to 5. For b5, the control sample sizes are again all equal and range from 1 to 5 but M ranges from 3 to 8. For lack of space, in this paper, we provide only the exact critical values (and the probabilities) at a-levels near 0.25, 0.1, 0.05, 0.01 and 0.001 where bl(l)3. The number of observations in each block, M, ranges from 3 to 8 and the sample sizes for the control group range from 1 to 2. A numerical example is given for illustration.

Keywords:

• randomized complete block design
• Mathisen's median test
• Mann-Whitney U statistic
• simple-tree alternatives
• many-to-one problem
• exact critical (and p-) values